Point Nine Repeating

A lot of people have problems with infinity. They think that infinity never happens and therefore anything that happens at infinity must be false. In calculus, we talk about limits that go to infinity and some people can't except that something infinite as being bounded in any way because you can never get to infinity there for any thing associated with infinity must be zero.

I remember these indeterminate forms from calculus. Anything that can be expressed as ∞ - ∞ or ∞ / ∞ or 0/0 is an indeterminate form. Just because ∞ - ∞ looks like zero, doesn't mean it is. Look at it this way.

Let X = ∞ - ∞, then X + ∞ = ∞. This is true for all real X. So we can't make the most intuitive guess, we have to settle for the fact we don't know.

So this leads me to the old boondoggle about .999999...=1.

I have had so many arguments with people that think that BOAT = SHIP, but can't accept .999999...=1. (Different sets of symbols representing the same concept.) And my opponents' argument is that 1 divided by ∞ > 0. Given that 1 - .99999... = .0000...01, which implies termination (which is impossible, but bear with me). So that the difference between the two numbers is 1 divided by some infinitely large difference. Of course, 1/∞ = 0, which means that 1=.99999....

Now you can say that there is always a little piece between the two numbers, but the numbers do meet at infinity and infinity is right where it should be: everywhere. So free yourself: accept that point nine repeating equals one.